Social-distancing measures were among the very few available policy responses to the initial outbreak of COVID-19, and they remain an important tool for containing recurring wavers of this and possible future pandemics. However, policies aiming at limiting the intensity of people-to-people contacts incur substantial socio-economic costs while their effectiveness varies over time and across locations. Having a robust way of measuring the level of people-to-people contacts and monitoring compliance with social-distancing policies would greatly aid governments in better calibrating their responses to future pandemic outbreaks. In this paper we use the case example of the Yandex's self-isolation index to explore the potential of composite indices that aggregate multiple sources of activity data collected by digital platforms as proxies for evaluating the people-to-people contact intensity. To this end, we propose two error-corrected autoregressive distributed-lag models, inspired by the classical SIR model of infectious disease dynamics, and use them in testing for cointegration between the self-isolation index and the official data on the numbers of new COVID-19 cases and deaths, for the two largest cities in Russia, Moscow and St. Petersburg. We have found evidence for such cointegration, which confirms that the COVID-19 epidemic curve can be explained by the level of people-to-people contact intensity as measured by the self-isolation index. Our findings suggest that the self-isolation index is a useful real-time indicator of the level of compliance with social distancing measures in the population and thus can serve as a reliable tool for informing policymaking.